`linprog` — Solve linear programming minimization problems with inequality constraints, equality constraints, and bounds.

linprog minimizes f' * x subject to A*x <= b, Aeq*x == beq, and lb <= x <= ub. Supported forms are x = linprog(f,A,b), x = linprog(f,A,b,Aeq,beq), x = linprog(f,A,b,Aeq,beq,lb,ub), and the two-, three-, and four-output variants.

Syntax

x = linprog(f, A, b)
x = linprog(f, A, b, Aeq, beq)
x = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval] = linprog(f, A, b)
[x, fval] = linprog(f, A, b, Aeq, beq)
[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub)

All supported linprog forms

x = linprog(f, A, b)
x = linprog(f, A, b, Aeq, beq)
x = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval] = linprog(f, A, b)
[x, fval] = linprog(f, A, b, Aeq, beq)
[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval, exitflag] = linprog(f, A, b)
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq)
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval, exitflag, output] = linprog(f, A, b)
[x, fval, exitflag, output] = linprog(f, A, b, Aeq, beq)
[x, fval, exitflag, output] = linprog(f, A, b, Aeq, beq, lb, ub)

Inputs

Name	Type	Required	Default	Description
`f`	`NumericArray`	Yes	—	Linear objective vector.
`A`	`NumericArray`	Yes	—	Inequality constraint matrix.
`b`	`NumericArray`	Yes	—	Inequality constraint right-hand side.
`Aeq`	`NumericArray`	No	`[]`	Equality constraint matrix.
`beq`	`NumericArray`	No	`[]`	Equality constraint right-hand side.
`lb`	`NumericArray`	No	`[]`	Lower bounds.
`ub`	`NumericArray`	No	`[]`	Upper bounds.

Returns

Name	Type	Description
`x`	`NumericArray`	Optimal decision vector.
`fval`	`NumericScalar`	Objective value f'*x at the solution.
`exitflag`	`NumericScalar`	Solver status code.
`output`	`Any`	Diagnostic metadata struct.

Returned values from linprog depend on how many outputs the caller requests.

Errors

Identifier	When	Message
`RunMat:linprog:InvalidArgument`	The argument count or optional argument grammar is invalid.	`linprog: invalid argument`
`RunMat:linprog:InvalidInput`	Objective, constraint, or bound dimensions/types are invalid.	`linprog: invalid input`

How `linprog` works

f, b, beq, lb, and ub must be numeric vectors with compatible lengths.
A and Aeq must be numeric matrices with one column per element of f.
[] may be passed for omitted optional Aeq, beq, lb, or ub arguments.
Typed-integer values in f, A, b, Aeq, beq, lb, or ub are role-specific RunMat extensions. Each value must be exactly representable as double before entering the host solver; otherwise the call errors instead of rounding silently.
Automatically resident inputs gather transparently for the host solver. Explicit gpuArray inputs are a RunMat extension and are rejected while strict compatibility mode disables extensions.
exitflag is 1 when an optimum is found, -2 when no feasible point is found, and -3 when the objective is unbounded below.
The fourth output is a struct with iterations, algorithm, constrviolation, and message fields.
Advanced MATLAB options, algorithms, problem structs, and lambda outputs are intentionally unsupported in this initial implementation.

Examples

Solve a bounded linear program

f = [-1; -2];
A = [1 1];
b = 4;
[x, fval, exitflag] = linprog(f, A, b, [], [], [0; 0], [])

Expected output:

x =
     0
     4
fval =
    -8
exitflag =
     1

Use equality constraints and lower bounds

f = [1; 2];
A = [];
b = [];
Aeq = [1 1];
beq = 3;
[x, fval] = linprog(f, A, b, Aeq, beq, [1; 0], [])

Expected output:

x =
     3
     0
fval =
     3

Use a finite lower bound on one variable

f = [1; 0];
[x, fval, exitflag] = linprog(f, [], [], [], [], [2; -Inf], [])

Expected output:

x =
     2
     0
fval =
     2
exitflag =
     1

Optimize along an equality face

f = [-1; 0; 0];
A = [1 0 0];
b = 1;
Aeq = [0 0 1];
beq = 0;
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq, [], [])

Expected output:

x =
     1
     0
     0
fval =
    -1
exitflag =
     1

Inspect infeasible status

[x, fval, exitflag, output] = linprog(1, [], [], [], [], 2, 1);
exitflag

Expected output:

exitflag =
    -2

Using `linprog` with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how linprog changes the result.

Run a small linprog example, explain the result, then change one input and compare the output.

FAQ

Does linprog support optimoptions or MATLAB problem structs?⌄

No. This implementation supports the common positional numeric call forms only.

Does linprog run on the GPU?⌄

No. It gathers automatically resident inputs and runs the active-set solve on the host. Explicit gpuArray solver inputs are accepted only when RunMat extensions are enabled.

Can linprog accept integer arrays?⌄

Only as gated RunMat extensions, independently for each solver role. Every integer value must be exactly representable in binary64; outputs remain double precision.

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how linprog is executed, line by line, in Rust.

View the source for linprog in Rust on GitHub
Learn how the RunMat runtime works
Found a bug? Open an issue with a minimal reproduction.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

`linprog` — Solve linear programming minimization problems with inequality constraints, equality constraints, and bounds.

Syntax

x = linprog(f, A, b)
x = linprog(f, A, b, Aeq, beq)
x = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval] = linprog(f, A, b)
[x, fval] = linprog(f, A, b, Aeq, beq)
[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub)

All supported linprog forms

x = linprog(f, A, b)
x = linprog(f, A, b, Aeq, beq)
x = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval] = linprog(f, A, b)
[x, fval] = linprog(f, A, b, Aeq, beq)
[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval, exitflag] = linprog(f, A, b)
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq)
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval, exitflag, output] = linprog(f, A, b)
[x, fval, exitflag, output] = linprog(f, A, b, Aeq, beq)
[x, fval, exitflag, output] = linprog(f, A, b, Aeq, beq, lb, ub)

Inputs

Name	Type	Required	Default	Description
`f`	`NumericArray`	Yes	—	Linear objective vector.
`A`	`NumericArray`	Yes	—	Inequality constraint matrix.
`b`	`NumericArray`	Yes	—	Inequality constraint right-hand side.
`Aeq`	`NumericArray`	No	`[]`	Equality constraint matrix.
`beq`	`NumericArray`	No	`[]`	Equality constraint right-hand side.
`lb`	`NumericArray`	No	`[]`	Lower bounds.
`ub`	`NumericArray`	No	`[]`	Upper bounds.

Returns

Name	Type	Description
`x`	`NumericArray`	Optimal decision vector.
`fval`	`NumericScalar`	Objective value f'*x at the solution.
`exitflag`	`NumericScalar`	Solver status code.
`output`	`Any`	Diagnostic metadata struct.

Returned values from linprog depend on how many outputs the caller requests.

Errors

Identifier	When	Message
`RunMat:linprog:InvalidArgument`	The argument count or optional argument grammar is invalid.	`linprog: invalid argument`
`RunMat:linprog:InvalidInput`	Objective, constraint, or bound dimensions/types are invalid.	`linprog: invalid input`

How `linprog` works

f, b, beq, lb, and ub must be numeric vectors with compatible lengths.
A and Aeq must be numeric matrices with one column per element of f.
[] may be passed for omitted optional Aeq, beq, lb, or ub arguments.
Typed-integer values in f, A, b, Aeq, beq, lb, or ub are role-specific RunMat extensions. Each value must be exactly representable as double before entering the host solver; otherwise the call errors instead of rounding silently.
Automatically resident inputs gather transparently for the host solver. Explicit gpuArray inputs are a RunMat extension and are rejected while strict compatibility mode disables extensions.
exitflag is 1 when an optimum is found, -2 when no feasible point is found, and -3 when the objective is unbounded below.
The fourth output is a struct with iterations, algorithm, constrviolation, and message fields.
Advanced MATLAB options, algorithms, problem structs, and lambda outputs are intentionally unsupported in this initial implementation.

Examples

Solve a bounded linear program

f = [-1; -2];
A = [1 1];
b = 4;
[x, fval, exitflag] = linprog(f, A, b, [], [], [0; 0], [])

Expected output:

x =
     0
     4
fval =
    -8
exitflag =
     1

Use equality constraints and lower bounds

f = [1; 2];
A = [];
b = [];
Aeq = [1 1];
beq = 3;
[x, fval] = linprog(f, A, b, Aeq, beq, [1; 0], [])

Expected output:

x =
     3
     0
fval =
     3

Use a finite lower bound on one variable

f = [1; 0];
[x, fval, exitflag] = linprog(f, [], [], [], [], [2; -Inf], [])

Expected output:

x =
     2
     0
fval =
     2
exitflag =
     1

Optimize along an equality face

f = [-1; 0; 0];
A = [1 0 0];
b = 1;
Aeq = [0 0 1];
beq = 0;
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq, [], [])

Expected output:

x =
     1
     0
     0
fval =
    -1
exitflag =
     1

Inspect infeasible status

[x, fval, exitflag, output] = linprog(1, [], [], [], [], 2, 1);
exitflag

Expected output:

exitflag =
    -2

Using `linprog` with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how linprog changes the result.

Run a small linprog example, explain the result, then change one input and compare the output.

FAQ

Does linprog support optimoptions or MATLAB problem structs?⌄

No. This implementation supports the common positional numeric call forms only.

Does linprog run on the GPU?⌄

No. It gathers automatically resident inputs and runs the active-set solve on the host. Explicit gpuArray solver inputs are accepted only when RunMat extensions are enabled.

Can linprog accept integer arrays?⌄

Only as gated RunMat extensions, independently for each solver role. Every integer value must be exactly representable in binary64; outputs remain double precision.

Optim

coneprog · fminbnd · fminunc · fsolve · fzero · integral · lsqcurvefit · lsqnonlin · optimoptions · optimset · quad · secondordercone

Elementwise

Trigonometry

acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh

Reduction

Structure

bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm

Signal

Rounding

ceil · fix · floor · mod · rem · round

Factor

chol · decomposition · eig · eigs · lu · qr · svd

Solve

cond · det · inv · linsolve · norm · null · pinv · rank · rcond · rref · vecnorm

Ops

cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose

Symbolic

digits · int · limit · piecewise · sym · syms · vpa

Fft

fft · fft2 · fftn · fftshift · ifft · ifft2 · ifftn · ifftshift

Interpolation

griddedInterpolant · interp1 · interp1q · interp2 · pchip · ppval · spline

Discrete

lcm · primes

Ode

ode15s · ode23 · ode45

Poly

polyder · polyfit · polyint · polyval · roots

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how linprog is executed, line by line, in Rust.

View the source for linprog in Rust on GitHub
Learn how the RunMat runtime works
Found a bug? Open an issue with a minimal reproduction.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

linprog — Solve linear programming minimization problems with inequality constraints, equality constraints, and bounds.

Syntax

Inputs

Returns

Errors

How linprog works

Examples

Solve a bounded linear program

Use equality constraints and lower bounds

Use a finite lower bound on one variable

Optimize along an equality face

Inspect infeasible status

Using linprog with coding agents

FAQ

Related Math functions

Optim

Elementwise

Trigonometry

Reduction

Structure

Signal

Rounding

Factor

Solve

Ops

Symbolic

Fft

Interpolation

Discrete

Ode

Poly

Open-source implementation

About RunMat

Download RunMat

linprog — Solve linear programming minimization problems with inequality constraints, equality constraints, and bounds.

Syntax

Inputs

Returns

Errors

How linprog works

Examples

Solve a bounded linear program

Use equality constraints and lower bounds

Use a finite lower bound on one variable

Optimize along an equality face

Inspect infeasible status

Using linprog with coding agents

FAQ

Related Math functions

Optim

Elementwise

Trigonometry

Reduction

Structure

Signal

Rounding

Factor

Solve

Ops

Symbolic

Fft

Interpolation

Discrete

Ode

Poly

Open-source implementation

About RunMat

Download RunMat

`linprog` — Solve linear programming minimization problems with inequality constraints, equality constraints, and bounds.

How `linprog` works

Using `linprog` with coding agents

`linprog` — Solve linear programming minimization problems with inequality constraints, equality constraints, and bounds.

How `linprog` works

Using `linprog` with coding agents